A quantitative analysis of the variational pattern of French loans in Luxembourgish showcasing R (and Quarto)

Perspectives on Linguistics

Peter Gilles

2026-03-02

The research question

Drawing on data from our Schnëssen project, we seek to understand the driving factors behind the choice of a variant of Germanic origin (Luxembourgish or German) or French origin.

Example:

• Germanic origin: Stréihallem, Strand, Ferndbedienung vs. French origin: Schallimo, Plage, Telecommande

This linguistic choice as the dependent variable is influenced by social or other linguistic variables as independent variables:

• age
• gender
• education
• language competencies (French, German)

Corollary aim of this presentation:

• showcase, how these questions will be adressed in a coherent and systematic way using R - for data wrangling and statistics -, Quarto - for writing-up and layout - and GitHub - for publishing and dissemination.

References/Tutorials

Statistics for Language Variation & Change with R

• LADAL - Language Technology and Data Analysis Laboratory
• https://lingmethodshub.github.io/
• (Levshina 2015)
• (Winter 2020)

Quarto

• https://quarto.org/

The data

Collected with Schnëssen app

• audio data for +800 linguistic variables inserted in translation tasks from German or French, image descriptions etc.
• per variable: 300 up to 1500 responses
• coded for variable, variant, social data of respondent

Sub-set for this study extracted as data frame/tibble in R.

# load and display the dataset
input_data <- readRDS("input_data.rds")

The dataset has 38452 rows.

Give an overview as table:

DT::datatable(input_data)

The tibble input_data has the following structure.

str(input_data)

Classes 'tbl_df', 'tbl' and 'data.frame':   38452 obs. of  16 variables:
 $ id               : Factor w/ 3151 levels "1000","1004",..: 393 452 508 555 726 783 811 821 828 849 ...
 $ variant          : Factor w/ 116 levels "Zwiwwel","Ënn",..: 1 1 2 2 1 2 2 2 2 2 ...
 $ variable         : Factor w/ 50 levels "Variant_Ënn",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ French_origin    : chr  "non-French" "non-French" "French" "French" ...
 $ domain           : chr  "lexicon" "lexicon" "lexicon" "lexicon" ...
 $ urbanity         : Factor w/ 3 levels "smaller towns",..: 1 1 2 1 1 1 1 2 2 1 ...
 $ socio_index      : Factor w/ 15 levels "(0.122,0.278]",..: 5 1 5 5 4 2 2 2 5 1 ...
 $ socio_index_raw  : num  0.89 0.243 0.821 0.856 0.594 ...
 $ region           : Factor w/ 5 levels "Norden","Osten",..: 3 4 2 4 3 4 3 4 2 4 ...
 $ first_language   : Factor w/ 1 level "Jo": 1 1 1 1 1 1 1 1 1 1 ...
 $ age6             : Ord.factor w/ 6 levels "≤ 24"<"25 bis 34"<..: 2 2 2 2 2 2 3 2 5 2 ...
 $ age              : Factor w/ 3 levels "young","middle-aged",..: 1 1 1 1 1 1 2 1 3 1 ...
 $ gender           : Factor w/ 2 levels "male","female": 2 2 1 2 2 2 2 2 2 2 ...
 $ education        : Ord.factor w/ 4 levels "other"<"Technical\nschool"<..: 4 4 4 4 4 4 4 4 3 4 ...
 $ competence_french: Factor w/ 3 levels "French\nlow",..: 3 2 2 2 2 3 3 2 3 3 ...
 $ competence_german: Factor w/ 3 levels "German low","German average",..: 3 3 3 3 3 3 3 3 3 3 ...

summary(input_data)

       id                   variant                         variable    
 1826   :   48   Kannapee       : 1188   Variant_Déierendoktesch: 1704  
 6398   :   48   Toilettëpabeier: 1126   Variant_Kannapee       : 1626  
 6410   :   48   Ënn            : 1120   Variant_Ënn            : 1589  
 1700   :   47   Kamäin         : 1087   Variant_Schaarschtech  : 1378  
 3818   :   47   Déierendokter  : 1045   Variant_Schallimo      : 1278  
 203    :   46   Kürbis         : 1034   Variant_Kürbis         : 1224  
 (Other):38168   (Other)        :31852   (Other)                :29653  
 French_origin         domain                        urbanity    
 Length:38452       Length:38452       smaller towns     :17007  
 Class :character   Class :character   rural areas       :16651  
 Mode  :character   Mode  :character   1\nStad Lëtzebuerg: 4794  
                                                                 
                                                                 
                                                                 
                                                                 
        socio_index    socio_index_raw      region      first_language
 (0.278,0.434]:11792   Min.   :0.1230   Norden : 4060   Jo:38452      
 (0.589,0.744]: 7396   1st Qu.:0.3434   Osten  : 6874                 
 (0.434,0.589]: 7380   Median :0.4746   Süden  :10643                 
 (0.122,0.278]: 5969   Mean   :0.4998   Zentrum:16875                 
 (0.744,0.9]  : 5619   3rd Qu.:0.6373   #ERROR!:    0                 
 (0.313,0.46] :   52   Max.   :0.8997                                 
 (Other)      :  244                                                  
        age6                age           gender     
 ≤ 24     : 7451   young      :17977   male  :11634  
 25 bis 34:10526   middle-aged:13313   female:26818  
 35 bis 44: 6799   old        : 7162                 
 45 bis 54: 6514                                     
 55 bis 64: 5106                                     
 65+      : 2056                                     
                                                     
                        education         competence_french  
 other                       :    0   French\nlow    : 2675  
 Technical\nschool           :13431   French\naverage:18193  
 Classical\nsecondary\nschool: 6881   French\nhigh   :17584  
 University                  :18140                          
                                                             
                                                             
                                                             
      competence_german
 German low    :  119  
 German average: 4377  
 German high   :33956  
                       
                       
                       
                       

What’s inside the tibble?

Using crosstables - Responses by age

table(input_data$age)

      young middle-aged         old 
      17977       13313        7162 

• Responses by age and French_origin

table(input_data$age, input_data$French_origin)

             
              French non-French
  young         6768      11209
  middle-aged   5229       8084
  old           3037       4125

• Responses by competence_french and French_origin

table(input_data$competence_french, input_data$French_origin)

                 
                  French non-French
  French\nlow        879       1796
  French\naverage   6776      11417
  French\nhigh      7379      10205

• Can we have this in percentages?

prop.table(table(input_data$competence_french, input_data$French_origin))

                 
                      French non-French
  French\nlow     0.02285967 0.04670758
  French\naverage 0.17621970 0.29691564
  French\nhigh    0.19190159 0.26539582

• Mean number of responses by id

mean(table(input_data$id))

[1] 12.20311

• How many different ids (= speakers) are in the dataset?

length(unique(input_data$id))

[1] 3151

The analysis

1st analysis: regression analysis

Hypothesis: The choice of a French variant (dependent variable/response variable) is influenced by social factors (independent variables/predictors).

Choice of regression analysis dependent on the nature of the dependent variable:

• binary: logistic regression
• count: Poisson regression
• continuous: linear regression

Our dependent variable French_origin is binary, thus we will use logistic regression.

Logistic regression

Prepare data

# see: https://slcladal.github.io/regression.html#Random_Effects
library(tidyverse)
library(lme4)
library(sjPlot)

data <- input_data %>%
  # filter for domain (lexicon or phonology)
  filter(domain == "lexicon") %>%
  # convert binary variable to values 0 and 1
  mutate(across(French_origin, str_replace, "non-French", "0")) %>%
  mutate(across(French_origin, str_replace, "French", "1")) %>%
  mutate(French_origin = as.integer(French_origin)) %>%
  mutate(age = factor(age, ordered = FALSE)) %>%
  mutate(age6 = factor(age6, ordered = TRUE)) %>%
  mutate(education = factor(education, ordered = FALSE)) %>%
  mutate(competence_german = factor(competence_german, ordered = FALSE)) %>%
  mutate(competence_french = factor(competence_french, ordered = FALSE)) %>%
  mutate(urbanity = factor(urbanity, ordered = FALSE))

The regression model will be fit step by step (‘stepwise regression’) by starting out with a base model without predictors and then adding one predictor after the other. After each step the model will be compared statistically with the previous one. If better, the predictor is retained, if the model is worse or the same, the predictor is eliminated. Step by step then the explanatory predictors are detected.

Logistic Regression

Fit base model. Use id and variable as random effects.

m0.lmer <- lmer(formula=French_origin ~ 1 + (1|id) + (1|variable), REML = T, data = data)

Add age as first predictor.

m1.lmer <- lmer(formula=French_origin ~ age + (1|id) + (1|variable), REML = T, data = data)
tab_model(m1.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.38	0.30 – 0.45	<0.001
age [middle-aged]	0.02	0.01 – 0.03	0.001
age [old]	0.04	0.03 – 0.06	<0.001
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.001 / 0.339

Compare which model is performing better.

anova(m1.lmer, m0.lmer, test = "Chi")

Data: data
Models:
m0.lmer: French_origin ~ 1 + (1 | id) + (1 | variable)
m1.lmer: French_origin ~ age + (1 | id) + (1 | variable)
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)    
m0.lmer    4 38443 38477 -19218    38435                         
m1.lmer    6 38411 38462 -19199    38399 36.505  2  1.183e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age is a significant contribution to the model. ✅ The age model is significantly better than the previous one.

Adding further predictors, starting with gender. Instead of refitting the model, we can update the model.

m2.lmer <- update(m1.lmer, .~.+ gender)
tab_model(m2.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.38	0.31 – 0.46	<0.001
age [middle-aged]	0.02	0.01 – 0.03	0.001
age [old]	0.04	0.03 – 0.06	<0.001
gender [female]	-0.01	-0.02 – 0.01	0.290
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.001 / 0.339

Compare again, which one is better.

anova(m2.lmer, m1.lmer, test = "Chi")

Data: data
Models:
m1.lmer: French_origin ~ age + (1 | id) + (1 | variable)
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + gender
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)
m1.lmer    6 38411 38462 -19199    38399                     
m2.lmer    7 38411 38471 -19199    38397 1.1189  1     0.2902

Gender is not significant. Remove it? Let’s try for the interaction with age.

m2.lmer <- update(m1.lmer, .~.+ gender*age)
tab_model(m2.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.38	0.31 – 0.46	<0.001
age [middle-aged]	0.02	-0.00 – 0.04	0.062
age [old]	0.04	0.01 – 0.06	0.003
gender [female]	-0.01	-0.02 – 0.01	0.388
age [middle-aged] × gender [female]	-0.00	-0.03 – 0.02	0.926
age [old] × gender [female]	0.01	-0.02 – 0.04	0.620
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.001 / 0.339

anova(m2.lmer, m1.lmer, test = "Chi")

Data: data
Models:
m1.lmer: French_origin ~ age + (1 | id) + (1 | variable)
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + gender + age:gender
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)
m1.lmer    6 38411 38462 -19199    38399                     
m2.lmer    9 38415 38492 -19199    38397 1.4425  3     0.6956

None of interactions is significant and the model is not performing better than the previous one. Gender will be removed ❌. Interestingly, and contrary to general sociolinguistic assumptions, gender seems to play no role in the choice of a French variant.

Add predictor competence_french.

m2.lmer <- update(m1.lmer, .~.+ competence_french)
tab_model(m2.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.32	0.25 – 0.40	<0.001
age [middle-aged]	0.01	-0.00 – 0.02	0.080
age [old]	0.03	0.02 – 0.05	<0.001
competence french [French average]	0.04	0.02 – 0.07	<0.001
competence french [French high]	0.09	0.06 – 0.11	<0.001
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.004 / 0.339

anova(m2.lmer, m1.lmer, test = "Chi")

Data: data
Models:
m1.lmer: French_origin ~ age + (1 | id) + (1 | variable)
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)    
m1.lmer    6 38411 38462 -19199    38399                         
m2.lmer    8 38324 38393 -19154    38308 90.154  2  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As expected, this is one is performing well. ✅

Maybe competence_french is interacting with age?

m3.lmer <- update(m1.lmer, .~.+ competence_french*age)
tab_model(m3.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.32	0.24 – 0.40	<0.001
age [middle-aged]	-0.00	-0.05 – 0.05	0.987
age [old]	0.07	0.00 – 0.14	0.047
competence french [French average]	0.05	0.02 – 0.07	<0.001
competence french [French high]	0.08	0.06 – 0.11	<0.001
age [middle-aged] × competence french [French average]	0.01	-0.04 – 0.06	0.771
age [old] × competence french [French average]	-0.04	-0.12 – 0.03	0.222
age [middle-aged] × competence french [French high]	0.02	-0.03 – 0.07	0.518
age [old] × competence french [French high]	-0.03	-0.10 – 0.04	0.427
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.004 / 0.339

anova(m3.lmer, m2.lmer, test = "Chi")

Data: data
Models:
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french
m3.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + age:competence_french
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)
m2.lmer    8 38324 38393 -19154    38308                     
m3.lmer   12 38330 38432 -19153    38306 2.7069  4      0.608

No interaction! Removed from the model. ❌

Add predictor competence_german.

m3.lmer <- update(m2.lmer, .~.+ competence_german)
tab_model(m3.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.34	0.22 – 0.46	<0.001
age [middle-aged]	0.01	-0.00 – 0.02	0.086
age [old]	0.03	0.02 – 0.05	<0.001
competence french [French average]	0.05	0.02 – 0.07	<0.001
competence french [French high]	0.09	0.07 – 0.11	<0.001
competence german [German average]	-0.02	-0.11 – 0.08	0.740
competence german [German high]	-0.02	-0.11 – 0.07	0.694
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.004 / 0.339

anova(m3.lmer, m2.lmer, test = "Chi")

Data: data
Models:
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french
m3.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + competence_german
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)
m2.lmer    8 38324 38393 -19154    38308                     
m3.lmer   10 38328 38414 -19154    38308 0.2494  2     0.8828

Not significant! Removed from the model. ❌

Add predictor education.

m3.lmer <- update(m2.lmer, .~.+ education)
tab_model(m3.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.31	0.24 – 0.39	<0.001
age [middle-aged]	0.02	0.00 – 0.03	0.013
age [old]	0.04	0.02 – 0.05	<0.001
competence french [French average]	0.03	0.01 – 0.06	0.002
competence french [French high]	0.07	0.05 – 0.09	<0.001
education [Classical secondary school]	0.04	0.02 – 0.05	<0.001
education [University]	0.03	0.02 – 0.04	<0.001
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.34
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.005 / 0.339

anova(m3.lmer, m2.lmer, test = "Chi")

Data: data
Models:
m2.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french
m3.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + education
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)    
m2.lmer    8 38324 38393 -19154    38308                         
m3.lmer   10 38297 38382 -19138    38277 31.709  2  1.302e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Education is a significant contribution to the model. ✅ Speakers coming from a classical school or university, use significantly more French variants.

Now adding predictors relating to the location of the speaker, starting with the degree of urbanity.

m4.lmer <- update(m3.lmer, .~.+ urbanity)
tab_model(m4.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.33	0.25 – 0.41	<0.001
age [middle-aged]	0.01	-0.00 – 0.02	0.095
age [old]	0.02	0.01 – 0.04	0.002
competence french [French average]	0.03	0.01 – 0.05	0.004
competence french [French high]	0.06	0.04 – 0.08	<0.001
education [Classical secondary school]	0.03	0.02 – 0.05	<0.001
education [University]	0.03	0.02 – 0.04	<0.001
urbanity [rural areas]	-0.03	-0.04 – -0.02	<0.001
urbanity [1 Stad Lëtzebuerg]	0.04	0.02 – 0.06	<0.001
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.33
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.007 / 0.339

anova(m4.lmer, m3.lmer, test = "Chi")

Data: data
Models:
m3.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + education
m4.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + education + urbanity
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)    
m3.lmer   10 38297 38382 -19138    38277                         
m4.lmer   12 38240 38343 -19108    38216 60.343  2  7.881e-14 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Urbanity is a ignificant contribution to the model! ✅ Check the algebraic sign for the estimates: In rural areas significant less French variants are used. In the capital significant more French variants are used.

Add predictor socio-economic index; ranges from 0 to 1 and is based on the share of single parents, mean salary, share of persons with RMG, level of unemployment per commune. 0 = favorable commune, 1 = defavorable commune (see STATEC).

m5.lmer <- update(m4.lmer, .~.+ `socio_index_raw`)
tab_model(m5.lmer)

	French_origin
Predictors	Estimates	CI	p
(Intercept)	0.38	0.30 – 0.46	<0.001
age [middle-aged]	0.01	-0.00 – 0.02	0.111
age [old]	0.03	0.01 – 0.04	<0.001
competence french [French average]	0.03	0.01 – 0.05	0.003
competence french [French high]	0.06	0.04 – 0.08	<0.001
education [Classical secondary school]	0.03	0.02 – 0.05	<0.001
education [University]	0.03	0.01 – 0.04	<0.001
urbanity [rural areas]	-0.04	-0.05 – -0.03	<0.001
urbanity [1 Stad Lëtzebuerg]	0.02	0.01 – 0.04	0.007
socio index raw	-0.08	-0.11 – -0.06	<0.001
Random Effects
σ2	0.15
τ00 id	0.01
τ00 variable	0.07
ICC	0.33
N id	3151
N variable	50
Observations	38452
Marginal R2 / Conditional R2	0.008 / 0.339

anova(m5.lmer, m4.lmer, test = "Chi")

Data: data
Models:
m4.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + education + urbanity
m5.lmer: French_origin ~ age + (1 | id) + (1 | variable) + competence_french + education + urbanity + socio_index_raw
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)    
m4.lmer   12 38240 38343 -19108    38216                         
m5.lmer   13 38206 38317 -19090    38180 36.432  1  1.581e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The socio-economic index is a significant contribution to the model. ✅ The higher the index, i.e. the less favorable the commune, the less French variants are used.

This is our final model. Speakers favoring French variants show the following social characteristics:

• rather old

• average to high competence in French

• education in classical school or university

• rather living in the capital, then in rural areas

• low socio-economic index

2nd analysis: correspondence regression analysis

See Plevoets (2020); Gilles (2023)

Run a regression with two predictors for all variants, instead for the variables. Group similar variants together in a two-dimensional space.

Run the correspondence regression analysis.

library(corregp)
corr.crg <- corregp(variant ~ competence_french * age, data=input_data,
                      part="variable", b=3000)

A Screeplot shows the amount of variation explained per so-called ‘latent variable’.

screeplot(corr.crg, add_ci=TRUE, type="%")

In this case, 65 % of variation is explained by the first ‘latent variable’ and 13 % by the second latent variable. A considerable amount of variation is thus explained through these two predictors, competence_french and age.

Now plot this in a two-dimensional space. Use green for variants with French origin and blue for variants with Germanic origin. In addition, plot also the values for age (young - middle-aged - old) and competence_french (low - average - high).

# Colors for plotting:
corr.col <- ifelse(xtabs(~variant + French_origin, data=input_data)[,"French"] > 0,
                       "green3", "blue")

plot(corr.crg, x_ell=TRUE, xsub=c("competence_french", "age"), col_btm=corr.col, col_top="orange",
     cex_btm=0.7, cex_top=0.7, font_btm= 1, font_top=2, hlim=c(-0.7,1.2), vlim=c(-0.3,0.6), 
     hlab = "Latent variable 1: 'xxx'", vlab = "Latent variable 2: 'xxx'", add_ori=TRUE)

French variants tend to concentrate in the NE quadrant, and Germanic variants more in the lower half. Interestingly, green and blue form - cum grano salis - two clouds. Distances become visible, e.g. Buttek associated with ‘French high’ and Geschäft with ‘French low’.

The end

• R will help you to understand your data and find the best statistical analysis

• Quarto will help you to write an analysis, a report or even an entire fully-fledged article in a journal layout - all in one place.

References

Gilles, Peter. 2023. “Regional Variation, Internal Change and Language Contact in Luxembourgish: Results from an App-Based Language Survey1.” Taal En Tongval 75 (1): 29–57. https://doi.org/10.5117/TET2023.1.003.GILL.

Levshina, Natalia. 2015. How to Do Linguistics with r: Data Exploration and Statistical Analysis. John Benjamins Publishing Company. https://doi.org/10.1075/z.195; http://web.archive.org/web/20200925101303/https://www.jbe-platform.com/content/books/9789027268457.

Plevoets, Koen. 2020. “Lectometry and Latent Variables: A Model for Underlying Determinants of (Normative) Choices in Written and Audiovisual Translations.” Zeitschrift Für Dialektologie Und Linguistik 87 (2): 144. https://doi.org/10.25162/zdl-2020-0006.

Winter, Bodo. 2020. Statistics for Linguists: An Introduction Using r. Routledge. https://www.taylorfrancis.com/books/9781315165547.